Getting at the quote in the post, it is a confused mixture of Boolean logic and set theory. If 'a' is truly a proposition, then atheists endorse the negation of that proposition, which is ~a. That's trivial within Boolean logic.

It's probably easiest to clean up the confusion by keeping it all in the language of set theory.

In the atheist's ontology, the set of gods is empty, while in the theist's ontology the set is nonempty. The sets don't include propositions at all, but objects (in this case gods).

So G={g} vesus G=Ø are the two competing claims, where g is not a proposition but an object.

In real conversations, it would probably be more useful to use an instance of this set theoretic claim in a real argument. E.g., Is your not believing in Zeus a religion?

On the other hand, 'religion' is a complex category defined along many dimensions. Many atheists fall on the 'religious' side of the values in that polydimensional semantic space.

It is easy to imagine not collecting stamps being a hobby (e.g., an anti-philatelist union could form, with meetings where people talk about the stupidity of stamp collecting).

I could also easily imagine groups of atheists forming that would satisfy many of the criteria of being a religion. You could get together every Sunday, have rituals to reinforce your belief that there are no gods, go door to door to spread this belief, etc..

However, not believing in gods is not sufficient to count one as being a member of a religion. More information would be needed about you before such a claim could be made.

This reminds me of a constant debate my friends and I have concerning "Big A Atheist" vs "Little a atheist," i.e. believing in the lack of existence of a God, vs the lack of a belief in the existence of God. People act like it's trivial, but I find it to be a very meaningful topic.

My thoughts on the topic:http://untitledvanityproject.blogspot.com/2010/08/oh-but-those-werent-real-atheists.html

It is NOT easy to imagine a "club" that forms discussing the stupidity of collecting stamps. You seem to be exceptionally deluded.

Philosophy[in your case imagination] is nothing but mental masturbation when it does not correspond to that annoying little thing we collectively agree to define as "reality". Just as masturbation, plz proceed to do it alone, and don't fill us in on the details.

If I understand correctly, this quote basically says atheism does not have any propositions! hmm! Is that a proposition? Where does it belong? in set S or T? or {}?

BTW, here are some examples of empty set from google search, "The set of dogs with six legs""The set of squares with 5 sides" , etcBy definition the reality described by the empty set does not exsit; So if atheism is empty set, thenthe reality described by this empty set (atheism) does not exit !!! Which implies God exists!!!

Are the pancakes any more nutritious because we bowed our heads, closed our eyes, folded our hands together and mumbled some words over them?

-------------------------

But seriously, folks...

If not, then how does anyone "manufacture" holy water? Or how does a Baptism have any effect? Or how does a recitation of the Last Rites help a mortally wounded soldier, other than to give him some small comfort as he awaits death?

And if spoken words have no effect other than what we ALLOW, then how do written words at some further remove from actualization have any authority over us except in that we ALLOW them to?

The oldest gospel (according to most biblical scholars) is Mark. Mark doesn't say anything about a virgin birth.

Matthew and Luke are widely regarded as embellishments on Mark, and both are commonly accepted to have been written late in the first century (c. 80-100 CE), and both give accounts of a virgin birth that neither of them could possibly have been around to know of firsthand.

Isaiah 7:14 used "almah", 'young woman', mistranslated "parthenos" in the LXX (and doesn't even refer to a future messiah), and now we have Matt and Luke proclaiming fulfilled prophecy, taken COMPLETELY out of context, and perpetuated in the Nicene Creed.

pink_monkey said:It is NOT easy to imagine a "club" that forms discussing the stupidity of collecting stamps. You seem to be exceptionally deluded.

pink_monkey, your crippled imagination is duly noted.

It is not easy to imagine a "club" that forms discussing the stupidity of theism. Oh. Wait.

My point was that merely knowing someone doesn't collect stamps isn't sufficient to know if not collecting stamps is a hobby for that person. If the person indeed started an anti-philatelist association and went door to door talking about this pastime, then it would count as a hobby.

no kidding, I find them weak at best. Again it is NOT easy to imagine a "club" that forms to discuss the idiocy of collecting stamps. Let me qualify that with in reality, since you seem to miss the point. Just as before, that's a very important qualification. In short, religion and hobbies are not analogous for reasons you pointed out yourself.

Atheism is the empty set. "a" does not exist in the atheist ontology, there is no possible way to endorse it's negation. Quit starting w/ the Theist worldview as the positive a priori. There is not even the proposition that deities exist w/in the Atheist paradigm. We're only defined as the opposite of theists[a-theists] precisely because theism enjoys special truth claims in this world. We don't start w/ "a" in an atheistic worldview and choose to not believe in it. There never was an "a". The theists have invented a set "a" for which the negation is meaningless. "Religious" Atheism [whatever that may mean] would be something else entirely.

object or proposition who cares can we really even put the God concept in words? Just because someone dreams up a whimsical set "a" that there is no evidence for in reality, I am not included in a set of those subscribing to "~a" because I reject their fantastical ideas. That's silly and meaningless. What I am is a member of an empty set, and they're just crazy. o0

BDK, I've had enough of your ignorance, not just here but elsewhere. Ignorance is what people express who try to force all people into conformity and force out diversity. Ignorance is a cookie cutter mentality, a church mentality, or groupthinking mentality. No, you're not ignorant about everything so don't expressed more ignorance about that which I just claimed.

You really think everyone should be like you, don't you? That's ignorance. What's further, it is complete and utter ignorance to say that people who are different than you are ignorant because they are different than you.

PZ Myers is an educated intelligent militant atheist and I posted a link to one of his talks recently. It is nonsensical for you to claim that more mature atheists should just lay back and not be passionate about their atheist because you are.

Get a grip. We are a diverse crowd. Take your cookie cutter utterly ignorant mentality elsewhere.

pink_monkey suggested that atheists have the absence of a belief in gods, not a positive belief that there are no gods. My response was that this site would attract few such "weak" atheists.

Where is my ignorance exactly?

Also, you are confused about what I dislike. I don't mind militant atheists at all. I think Dawkins is incredibly entertaining and witty, have enjoyed the work of Harris.

What I mind is your willingness to substitute name-calling for real argument, your tendency to overstate the originality and strength of the arguments that you do present (e.g., the outsider test). You are just awful at the give-and-take of real argumentation, as evidenced by how you dealt with Reppert/McGrew recently. I mind that you hypocritically hammer people that you think don't have credentials, but then act as if your lack of serious specialization (i.e., PhD) shows you are some kind of intellectual jack of all trades poised to be especially damaging to the Christian philosophy. The shameless plugging of your books doesn't do anything for your credibility either, whether or not it helps sales.

So, John, my problem isn't militant atheists: it's you. You are taking on the roll of a public face of atheism, and you make us look arrogant and incapable of logical argument. It is embarrassing to have you out there implicitly representing something I believe personally, and doing such a crappy job of it.

With your actions on the blogosphere, you are giving the Christians as much ammunition as you think you are giving them doubt. You are to atheism what that crazy communist lady on the corner handing out 9-11 conspiracy pamphlets is to progressivism.

BDK, I did over-react, yes, because you are a buffoon and I'm tired of you. You do not know enough about me to be able to make those claims.

It never crosses your mind that the reason Christians attack me is because they think I'm a threat, does it? And it never crosses your puny mind that I have an ugly history with certain Christian people on the web, does it? And it never crosses your puny mind that I have tried various ways to deal with Christians who have verbally assaulted me to no avail. And it never crosses your puny mind how often I am personally attacked. And so it never crosses your puny mind how you would respond if you were me. You see, they don't just call my arguments ignorant and utterly stupid, which they do. They also repeatedly mischaracterize my arguments to show that they are stupid. They also call me a wicked person and make up stuff up about me that isn't true. Which you have bought into the smear campaign.

You are the ignorant one, completely ignorant about me. Stay away from here. Wear it as a badge.

Appearances can be deceiving. Read through DC if you care to be informed. There is a Christian smear campaign against me and it has convinced people I am what they say.

And so just because Reppert and Hays have agreed to settle their own personal war by agreeing to attack me doesn't mean that I must respond civilly to these attacks which have gone on now for over four years on a weekly and at some points even a daily basis.

All you do is step into one of these threads and see something going on at the end of years of abuse. Couple that with what you read elsewhere stemming first from Christians and then form skeptics who have bought into it you think you found the evidence you need to believe it.

You haven't. You are shooting me from the rear just exactly like Christians who fear me have hoped for.

I have been posting and reading at Vic's blog since 2005. My first post there I was basically a dick (it is in this thread and then I realized that Victor wasn't your typical ostrich evangelical Christian I ended up apologizing).

He is a fair interlocutor, I have clashed with him many times quite vociferously. While I have not convinced him I am right, he has shown sensitivity to my arguments over time, revised his claims, at least shown a good-faith effort to engage with the arguments. He seems to have done the same with you, but I am less tuned in than you, admittedly.

I have never seen him mock or ridicule you. Maybe he hasn't read your book, or done all the historical scholarship (at least that's what you and others claim about him: I wouldn't know, frankly). But that is very different from "abuse". If you were talking about Bill Valicella I'd buy it, but Victor? Come on.

Okay, then, maybe not abuse, but Vic baits me by micharacterizing me. There are circles people run in and Vic runs with Steve Hays. Hays posted something against every single post I made for about six months, calling it trash, garbage, and filled with idiocies. That's every single post for about six months. Vic eventually adopted Hays attitude toward my arguments and decided my book was probably nothing new based on what Hays wrote and probably stupid too. Now if you know anything at all about Hays there are no good arguments against his faith. They are all stupid or they have been refuted a long time ago.

So here's how it's worked ever since. Vic posts something that mischaracterizes my position (because he has not read my book and takes snippets from my blog), I respond, Steve attacks. Vic knows Steve will respond as do I. Why do I respond to this baiting? Because I do not want to be mischaracterized by someone like Vic who is a Christian philosopher, especially since I consider him ignorant.

Now you have seen what you've seen in the midst of this history and you have concluded my arguments are ignorant based upon Vic's judgements who has not read my book(s) because of the judgment of Hays who thinks all arguments against his faith are stupid ones.

And so after I answer them sometimes I go there to blast them. It's like the proverb "don't cast your pearls before the swine. Although, I've decided not to do so ever again. They can take more potshots but I don't plan on responding. They deserve each other. And if you stay there you all deserve each other.

OK: what is the worst mischaracterization of what you say, and what is the source of the original argument that they are mischaracterizing? I do remember Hays tends to write long-winded crazy rambles, and did recently at the post where you got a bit out of control. Hayes ≠ Reppert, of course, but Reppert does like to get conversations going between people that disagree.

Vic is extremely critical of Hays as well. They have attacked one another's ideas quite often (e.g., about Calvinism/determinism). It seems you are reading too much into it.

my point BDK was that we wouldn't be forced to have a strong belief in the non existence of deities if the Theist worldview wasn't so entrenched. We are forced to a meaningless negation a priori. In reality we are the empty set. In western society we are the set "~a" despite the fact that the set "a" does not exist so there can be no negation. Get it?

And I didn't come here because of my lack of belief in God's, it was quite the opposite. I, like many here, came because the house of cards that is Christianity began displaying cracks. John's books and his blog, as well as the many spirited "commenters" here helped me to transition to a declaratory Atheistic position. Family and friends don't always take too kindly to my position so it can be nice to read and discuss ideas w/ the people who frequent this site. They are not all militant Atheists, and John did not design this site for Militant Atheism explicitly. He designed it for people like me, and Chuck, and Hendy, people who were "snowed" and began to see the light w/o the delusion. I am grateful for this site, and others like it across the web, as well as the people who frequent them. We need to combat the misinformation. That's really the purpose here, despite the fact that tempers often flair[c'mon...dealing w/ creotards is hardly easily done]. So thank you John for your efforts, you have helped me, and I appreciate that. I don't think John gets thanked quite often enough.

That being said we need Militant Atheists, and I tend to be one most times. At least the discussion is becoming more widespread and hopefully Atheism less of a dirty word. Force is necessary for movements to take a foothold, history illustrates this beautifully. The cracks in Theism are being exposed, and w/ any luck we will one day exist in a society where Militant Atheism is unnecessary. We truly will be the empty set that thus far eludes us. I "pray" that day comes, but today is not it.

And lighten up on John. Anyone who knows anything about Atheists knows that we can hardly be represented by one person[the theists know this too]. We are by nature an eclectic mix. Find contentment in the fact that John and others are speaking out to make Atheistic views more acceptable w/in society. I feel privileged to live in this moment, in the thick of this movement. Humankind will finally break free from it's Theist shackles, and that's really what we all want. Stand with them, applaud them, thank them.

she obviously didn't read the full thread; at least not the parts where I think I properly explained that.

I'm sick of the a priori assumption; it rears it's ugly head again on the Hawking quote[cneil pts it out nicely].

and sorry ed for not including you in my rant to brad/noc about outspoken ppl from this site. You have made too many good points to be excluded. I forgot you since you're relatively new[as I am to you], but I've been lurking quite awhile.

And "no", christian trolls, I am not a figment of John's imagination. I know he gets accused of that now and again when someone shows up in his defense. First off, i'm not his style...secondly, he really is a likable guy and I really do appreciate his work. To your chagrin, people like me really do exist, and in masses. You'll be hearing from us more and more. Thank "God".

i just wanted to say that I love gandolf[and no i'm not really[at least Loftus didn't make to behave in that way] the bi-curious sam from lord of the rings]. Too many [ ]...shoulda used a { } or ( )... keep on keepin on gandy, you have my full support.

also, sorry for forgetting you too shane...i seem to be fairly forgetful.

sry guys and ty, gj[i should say gg since the theists have reduced it to that]. 0o

In cases where an atheist ( and in my experience, this does happen, and quite often at that) states " God does not exist"; " God is fiction" ; " There is no such thing as God ";etcwhy does he/she insist on laying claim to set { } and reject being characterized by set {~a} ?

p.s. keeping in mind the other critique I have of the original quote:( if "a" means "A deity exists", then "~a" should mean "The said deity does not exist", NOT, " no deities exist").

you need to re-read this thread and then direct your comments at me, since i made the post you are referring to. You don't seem to be comprehending my argument.

Are you aware of what an a priori assumption of God entails?

Seen through a purely atheistic ontology god does not exist. There is no negating any deities from this perspective. The set is empty and {a} or {~a} are meaningless. Because the majority of western society accepts the set {a} a priori, and coerces us atheists into a set {~a}, this says nothing about the actual atheistic worldview. Get it now?

you really should still reread this thread for comprehension. it's you christians that force militant atheism upon yourselves.

>>You need to re-read this thread and then direct your comments at me, since I made the post you are referring to.<<

It is useful to re-read parts of this thread. It is not useful to re-read the full thread, as not all posts are directly related to my question.

And my questions/ comments can be directed towards ANYONE (not just you) who does say something to which my question relates.

I find it curious that you said (in reference to my first post):

"she obviously didn't read the full thread; at least not the parts where I think I properly explained that."

pink_monkey, tell me what statement of yours had answered the question:

"If {a} = theism and { } = atheism , then what DOES {~a} equal ?"

(anotherway to have put it: What term describes a person belonging to set {~a}? )

FYI, Complaining about the 'meaninglessness' of two of the sets does not answer the question.

I appreciate GearHedEd's response to me (though I disagree with it) because HE began with :"The set {~a} would denote someone..."

Which is an good example of an answer that is RIGHT TO THE POINT.

>>Because the majority of western society accepts the set {a} a priori, and coerces us atheists into a set {~a}...<<

It does not coerce you, as an a priori assumption entails 3 options:

1) Agreement2) Uncertainty3) Disagreement

Disagreement <=> {~a}

The point I was making in my second post, is that there are atheists who speak out of both sides of their mouth.

On the one hand saying " I don't have positive belief in the non-existence of God, I merely lack belief in God" (thus claiming an empty set) and on the other hand saying that "God is the result of human imagination ."

To claim that something is the result of imagination, is a euphemism for saying something is not real. IF YOU ARE GOING TO CLAIM THAT SOMETHING IS NOT REAL, YOU ARE ASSERTING ~a.

If you MERELY claim, that something is UNPROVEN (which is very different from DISPROVEN), then you DO NOT fall under the set {~a}.

If people are going to use the concepts of unproven and disproven interchangeably, then they ought not be offended when they are characterized by set {~a}.

Also see Blue Devil Knight's first post in this thread, which pointed out the "confused mixture of Boolean logic and set theory" in Michael's original statement that you quoted (and the original thread which is linked to on the main page).

And likewise, you found problems in Michael's original quote:

"...p.s. keeping in mind the other critique I have of the original quote:( if "a" means "A deity exists", then "~a" should mean "The said deity does not exist", NOT, " no deities exist")."

So what's the problem? We (nate and I) clarified something you already identified as problematic.

I had read BDK's post, so I'm aware he also offered critique of Michael's quote.

But my original post GRANTED Michael his claim about the sets, so that I could ask my question (which by itself assumes that Michael's claim is correct).

I asked it because Michael made a claim about what {~a} IS NOT (atheism). He never clarified what {~a} IS.

Your response to my question was to the point. You said:

"The set {~a} would denote someone who is anti-God (against an extant God), as opposed to the proper atheist empty set { }."

The reason I disagree with it is,because if I were to call someone - who says something to the effect of "God does not exist", -'anti-God', that person would talk about how they can't be anti or against something that doesn't exist.

>>So what's the problem? <<

I summed it up in my third post.Read from where it says

"The point I was making in my second post, is that there are atheists who speak out of both sides of their mouth. "

I have a problem with this (original) claim, similar to what BDK said. Michael's statement is somewhat garbled.

I might, if I felt like tackling it reconstruct it thus:

Theism is Set 'T'= {a}, where "a" denotes belief in an extant god (or gods),

Atheism is Set 'A'= [~a}, where "~a" denotes a belief that there are NO extant gods

(Note that neither statement addresses the topic of "proof", only statements of belief, as it should have been formulated in the first place.)

To delve into questions of proof is another game entirely, and Michael's statement is garbled for this reason:

Theism does not equal "A deity exists".

Theism is a belief system in which it is accepted (believed) that a deity exists.

Likewise, atheism (Atheism should never be capitalized unless it is at the beginning of a sentence) does not equal "There is no such thing as God (or gods)". Atheism is a belief system that does not accept the concept of gods as being real.

Like BDK said,

"...It's probably easiest to clean up the confusion by keeping it all in the language of set theory.

In the atheist's ontology, the set of gods is empty, while in the theist's ontology the set is nonempty. The sets don't include propositions at all, but objects (in this case gods)."

But here we're moving to objects rather than beliefs, and it then follows that for theists, the set of deity(-ies) vs. the set for atheists is the statement

"G={g} vesus G=Ø", where "g" denotes God or gods, and "Ø" is an empty set containing no god(s).

The objections you keep raising have been handled many times in this thread in a variety of ways. Your lack of comprehension is baffling to me. Noone is speaking out of both sides of their mouth.

You don't seem to understand what it means to assume the theist stance a priori, nor do you appear to be aware of what an atheistic ontology entails. IMO, this was explained in this thread in great detail. I'm really not sure why you keep begging for a definition of {~a} when it has been defined consistently multiple times.

And yes ana, when I suggested that you re-read the thread[which you still should do], what I meant was to read the parts where BDK was fighting w/ John, and concentrate on them. I really did think that those parts would answer your question.

Anyway, thanks for illustrating that it is futile to address you, i'll remember that for the future. Ed seems to have more patience this time, and he's doing a fine job of it anyway.

Do you think I was categorizing ALL atheists as speaking out of both sides of their mouth? Or that I was alluding to someone on this thread as doing such?

>>I'm really not sure why you keep begging for a definition of {~a} when it has been defined consistently multiple times.<<

I did not ask for a definition.

I already saw what {~a} MEANS ( "no deities exist") ORas GearHeadEd suggested("a belief that there are NO extant gods").

A meaning (i.e. definition) of {~a} had already been offered. I KNOW THAT.

"Armed fighting between two groups" is a definition. "War", is its word.

I was interested in knowing if there was a WORD attached to the definition of {~a}

(because if there is a word, Michael didn't tell us what it is)

I will repeat this one last time. My question was, WHAT DO YOU CALL A PERSON THAT IS CHARACTERIZED BY SET {~a}. Is there an established SINGLE-WORD that describes such a person? An "__ist" of some kind?

Now do you get it?

>>what I meant was to read the parts where BDK was fighting w/ John, and concentrate on them. I really did think that those parts would answer your question<<

I read those parts, and they did not answer my question. The exchange between them went beyond what the original post was about, and even got personal. I am not interested in such. If I was, my comments would have been directed towards that exchange.

>>Anyway, thanks for illustrating that it is futile to address you, i'll remember that for the future.<<

Let me tell you what you really need to remember for the future.

You need to really remember that ifyou ever come across a person who raises a question that YOU think has already been answered in the thread, then it should be easy enough for you to copy and paste that answer in response to the person's question.

Lest the person take your vagueness as evidence that the answer to the question, was in fact, absent in the thread.

copy and past the preceding entry, i'll have to remember that. perhaps reading for comprehension is all that's really necessary but what do I know.

so my sarcasm isn't lost again, this was indeed sarcastic.

now please re-read my previous post[I don't know why you won't trust my much better informed position on this issue and just re-read when I tell you to], note where I was unusually sarcastic, and LOL at yourself. I still am.